A new Bookstore website receives 13 hits each day The probab

A new Bookstore web-site receives 13 “hits” each day. The probability that a “hit” results in a purchase is 0.3300. Use Excel to calculate the probability and cumulative probability tables for this binomial experiment. Format the cells to four decimal places. Then, answer the following questions.

a. Compute the expected value, E(x)

d. Thirteen people enter the site … what is the probability that exactly three make a purchase?

e. Thirteen people enter the site … what is the probability that fewer than six make a purchase?

f. Thirteen people enter the site … what is the probability that at least four make a purchase?

g. Thirteen people enter the site … what is the probability that no more than six make a purchase?

h. Thirteen people enter the site … what is the probability that more than nine make a purchase?

i. Thirteen people enter the site … what is the probability that any number except eight make a purchase?

j. Thirteen people enter the site…what is the probability that more than four but fewer than eight make a purchase? (Hint: This could also be stated as 5, 6, or 7 make a purchase.)

Be sure everything is in order, numbered and neat. Don’t break your table output across pages

Solution

Normal Distribution
a)
Mean ( np ) =13 * 0.33 = 3.9
b)
variance ( npq )= 13*0.3*0.7 = 2.73
c)
Standard Deviation ( npq )= 13*0.3*0.7 = 1.6523
          
d)
P( X = 3 ) = ( 13 3 ) * ( 0.33^3) * ( 1 - 0.33 )^10
= 0.1874
e)
P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 13 5 ) * 0.33^5 * ( 1- 0.33 ) ^8 + ( 13 4 ) * 0.33^4 * ( 1- 0.33 ) ^9 + ( 13 3 ) * 0.33^3 * ( 1- 0.33 ) ^10 + ( 13 2 ) * 0.33^2 * ( 1- 0.33 ) ^11 + ( 13 1 ) * 0.33^1 * ( 1- 0.33 ) ^12 + ( 13 0 ) * 0.33^0 * ( 1- 0.33 ) ^13   
= 0.7669
f)

P( X < 4) = P(X=3) + P(X=2) + P(X=1) + P(X=0) +
= ( 13 3 ) * 0.33^3 * ( 1- 0.33 ) ^10 + ( 13 2 ) * 0.33^2 * ( 1- 0.33 ) ^11 + ( 13 1 ) * 0.33^1 * ( 1- 0.33 ) ^12 + ( 13 0 ) * 0.33^0 * ( 1- 0.33 ) ^13 +   
= 0.3317
P( X > = 4 ) = 1 - P( X < 4) = 0.6683
g)
P( X < = 6) = P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 13 6 ) * 0.33^6 * ( 1- 0.33 ) ^7 + ( 13 5 ) * 0.33^5 * ( 1- 0.33 ) ^8 + ( 13 4 ) * 0.33^4 * ( 1- 0.33 ) ^9 + ( 13 3 ) * 0.33^3 * ( 1- 0.33 ) ^10 + ( 13 2 ) * 0.33^2 * ( 1- 0.33 ) ^11 + ( 13 1 ) * 0.33^1 * ( 1- 0.33 ) ^12 + ( 13 0 ) * 0.33^0 * ( 1- 0.33 ) ^13   
= 0.9012

Note: Post the remaning parts in next question